Prepare all ingredients as described above.

Season the shaved steak with salt and pepper.

Heat the olive oil in a pan over medium heat. Add the sliced onions and sauté until softened and beginning to brown.

Add the shaved steak to the pan and cook until nicely browned.

In a small pot, combine the beef broth and rosemary. Bring to a simmer and cook for 15–20 minutes to allow the flavors to develop. Stir in the butter and taste. Adjust seasoning with salt and pepper if desired.

Preheat the oven broiler to low. Slice the rolls open and place them on a baking sheet. Toast under the broiler until golden brown, watching closely to prevent burning.

Using tongs or a slotted spoon, dip the cooked beef into the au jus, then portion the beef onto the toasted rolls.

Optional: Top each sandwich with provolone cheese and melt briefly under the oven broiler.

In a glass, combine sparkling water with sliced lemon and stir gently. Serve over ice if desired.